Question

In a certain population, 25% of the person smoke and 7% have a certain type of heart disease. Moreover, 10% of the persons who smoke have the disease.

What percentage of the population smoke and have the disease?

What percentage of the population with the disease also smoke?

Answer 1

Solution:

Given: In a certain population, 25% of the person smoke and 7% have a certain type of heart disease.

Let S = Smoker  

Thus we have:

P( Smoke ) = P(S) = 25% = 0.25

and

Let D = have heart disease  

thus we have:

P(Disease ) = P(D) = 7% = 0.07

Also we have :

P( Disease given smoke ) = P( D | S ) = 10% = 0.10

Part a) We have to find:

P( smoke and have the disease ) = .............?

P( S and D) = ..............?

Using conditional probability formula we get:

That is:

that is:

Thus 2.5% of the population smoke and have the disease.

Part b) We have to find:

P( the population with the disease also smoke) = ............?

P( S | D) = .............?

Using conditional probability formula we get:

From part a) we have P( S and D) = 0.025

Thus

Thus 35.71%  of the population with the disease also smoke.